Bulletin of the Seismological Society of America, Vol. 100, No. 1, pp. 225–240, February 2010, doi: 10.1785/0120090028
Ⓔ
A California Statewide Three-Dimensional Seismic Velocity
Model from Both Absolute and Differential Times
by Guoqing Lin,* Clifford H. Thurber, Haijiang Zhang,† Egill Hauksson, Peter M. Shearer,
Felix Waldhauser, Thomas M. Brocher, and Jeanne Hardebeck
Abstract
We obtain a seismic velocity model of the California crust and uppermost
mantle using a regional-scale double-difference tomography algorithm. We begin
by using absolute arrival-time picks to solve for a coarse three-dimensional (3D) P velocity (V P ) model with a uniform 30 km horizontal node spacing, which we then use as
the starting model for a finer-scale inversion using double-difference tomography
applied to absolute and differential pick times. For computational reasons, we split
the state into 5 subregions with a grid spacing of 10 to 20 km and assemble our final
statewide V P model by stitching together these local models. We also solve for a statewide S-wave model using S picks from both the Southern California Seismic Network
and USArray, assuming a starting model based on the V P results and a V P =V S ratio of
1.732. Our new model has improved areal coverage compared with previous models,
extending 570 km in the SW–NE direction and 1320 km in the NW–SE direction. It also
extends to greater depth due to the inclusion of substantial data at large epicentral
distances. Our V P model generally agrees with previous separate regional models
for northern and southern California, but we also observe some new features, such
as high-velocity anomalies at shallow depths in the Klamath Mountains and Mount
Shasta area, somewhat slow velocities in the northern Coast Ranges, and slow anomalies beneath the Sierra Nevada at midcrustal and greater depths. This model can be
applied to a variety of regional-scale studies in California, such as developing a unified
statewide earthquake location catalog and performing regional waveform modeling.
Online Material: Smoothing and damping trade-off analysis, a priori Moho depth,
resolution tests, and map-view slices and cross sections through the 3D V P and V S
models.
Introduction
model for locating earthquakes in California. In this study,
we take advantage of the regional-scale double-difference
(DD) tomography algorithm (Zhang and Thurber, 2006) to
develop P- and S-wave velocity models for the entire state
of California. Our P velocity model is derived from both
first-arrival absolute and differential time picks obtained from
the California seismic networks and has a horizontal grid
spacing as fine as 10 km. The S velocity model is solved using
the SCSN and USArray picks with a horizontal grid spacing
of 30 km. There are numerous tomographic studies in
California and it is impractical to compare our model with
all of them; we focus on a comparison with the recent
regional-scale tomographic studies for southern and northern
California by Lin et al. (2007) and Thurber et al. (2009).
Because our V P and V S models are solved using different sets
of data and the V P model has better resolution, we present
Numerous studies of velocity structure in California have
been done with varying scales in different areas (Table 1).
The largest and most complete crustal tomography models
in California are the recent southern California model by
Lin et al. (2007) and the northern California model by Thurber
et al. (2009). These studies have revealed key features of the
crustal structure of California. The integration of the Northern
and Southern California Seismic Networks (NCSN and SCSN)
into a unified statewide network, the California Integrated
Seismic Network (CISN; e.g., Hellweg et al., 2007), has
motivated the development of a statewide seismic velocity
*Now at Division of Marine Geology and Geophysics, Rosenstiel School
of Marine and Atmospheric Science, University of Miami, Miami, Florida,
33149 ([email protected]).
†
Also at Department of Geoscience, University of Wisconsin–Madison,
1215 W. Dayton St., Madison, Wisconsin 53706.
225
226
G. Lin, C. H. Thurber, H. Zhang, E. Hauksson, P. M. Shearer, F. Waldhauser, T. M. Brocher, and J. Hardebeck
42˚
s
h
at tain
am n
Kl Mou
Mount Shasta
A
Volcanic Plateau
Lake Shasta
Lake Almanor
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Fracture
Zone
Lake
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d
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W
te
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M
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ai
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ou
ific
F
SA
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an
34˚
Mojave Desert
SA
F
SG
Landers
Northridge M
SMM
WN
Los
Angeles
SBM
an
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San
Diego
IM
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ula
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ins
n
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California
Continental
Borderland
GF
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ad rn
ev lifo
a
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SSJV
Death
Valley
Coso
N
Parkfield
Cholame
Valle y
ra Nevada
36˚
Sier
B
Owens
F
k
oc
s
ey
Bl
ge
all
t V Ran
n
ia
st
ea
lin
Gr Coa
Sa
SA
SFB
C’
a
San
Francisco
38˚
Basin
and
Range
Province
B’
Lake
Tahoe
GV
HRC
lt
Fau nges
a
ma
aca ast R
Ma
Co
40˚
Baja California
32˚
200 km
A’
-126˚
-124˚
-122˚
-120˚
-118˚
-116˚
-114˚
Figure 1. Map of selected geological and geographic features in our study area. The thick straight lines indicate the model cross sections
shown in Figure 7. The NW–SE profile A-A’ is parallel to the San Andreas fault, and the SW–NE profiles B-B’ and C-C’ are perpendicular to
the San Andreas fault. Abbreviations: E, Elsinore fault; GF, Garlock fault; GV, Green Valley fault; HRC, Healdsburg–Rodgers Creek
fault; IM, Imperial Valley fault; SAF, San Andreas fault; SBM, San Bernardino Mountains; SFB, San Francisco Bay; SGM, San Gabriel
Mountains; SJ, San Jacinto fault; SMM, Santa Monica Mountains; SSJV, Southern San Joaquin Valley; TR, Transverse Ranges; VB, Ventura
basin; WN, Whittier Narrows.
them separately with more emphasis on the V P model.
Figure 1 shows selected geological and geographic features
in our study and the positions of three profiles for the velocity
cross sections.
P-Wave Velocity Model
Data and Inversion Method
The data sets for our V P model are the first-arrival
absolute and differential times of 8720 earthquakes recorded
by the seismic networks in California, consisting of 4325
events from the Northern California Seismic Network,
3668 events from the Southern California Seismic Network,
and 727 events from the Pacific Gas and Electric seismic
network (blue, pink, and green dots in Fig. 2a, respectively).
These earthquakes were selected based on having the greatest number of P picks among those events within a 6 km
radius, with a magnitude threshold of 2.5. The total number
of P picks in our data set is 551,318 with an average of 63
picks per event. In order to improve constraints on the shallow crustal structure, we assembled first-arrival times from
3110 explosions and airguns (red circles in Fig. 2b) recorded
on profile receivers and network stations. The principal
active-source data sets and sources are listed in Table 2.
A California Statewide Three-Dimensional Seismic Velocity Model
(a)
earthquake from NCSN
earthquake from PG&E
earthquake from SCSN
42˚
227
(b)
shot
quarry blast
42˚
40˚
40˚
38˚
38˚
36˚
36˚
34˚
34˚
32˚
32˚
200 km
30˚
-126˚
-124˚
200 km
-122˚
-120˚
-118˚
-116˚
-114˚
(c)
30˚
-124˚
-126˚
-122˚
-120˚
-118˚
(d)
0
42˚
40˚
grid node
5
x
Depth (km)
42˚
-114˚
-116˚
10
15
20
25
40˚
30
0
3
60
y=
38˚
38˚
4
5
6
7
8
Vp (km/s)
0
45
y=
0
30
y=
36˚
36˚
0
15
y=
Y
34˚
0
y=
34˚
50
-1
y=
-124˚
-122˚
0
-126˚
0
18
-114˚
0
-116˚
x=
-118˚
90
x=
-120˚
-120˚
80
-122˚
-1
-124˚
00
-6
y=
0
-9
-126˚
30˚
x=
30˚
50
-4
y=
200 km
x=
200 km
x=
y=
32˚
27
x=
00
-3
32˚
-118˚
-116˚
-114˚
Figure 2. Event and station distributions in our study area and starting inversion grid nodes for the 3D coarse model (30-km horizontal
spacing). (a) earthquakes; (b) controlled sources; (c) stations; (d) inversion grid nodes (small panel shows the 1D starting velocity model).
Quarry blasts, which have known locations but unknown origin times, are also valuable to be included in tomographic
inversions because they provide constraints that are almost
as good as the active-source data. We include data from
44 quarry blasts (blue circles in Fig. 2b), with 19 in southern California (see Lin et al., 2007) and 25 in northern
California. Figure 2c shows the locations of temporary and
network stations used in our study.
The model presented in this study is obtained by using a
regional-scale DD tomography algorithm (tomoFDD; Zhang
and Thurber, 2006), which is a generalization of DD location
(Waldhauser and Ellsworth, 2000). It maps a sphericalEarth coordinate system into a Cartesian coordinate system
(a sphere in a box; Flanagan et al., 2007) and incorporates a
finite-difference travel time calculator and spatial smoothing
constraints. This algorithm is designed to solve jointly for 3D
velocity structure and earthquake locations using both firstarrival times and differential times, leading to improved resolution in the seismically active areas where the differential
data provide dense sampling.
228
G. Lin, C. H. Thurber, H. Zhang, E. Hauksson, P. M. Shearer, F. Waldhauser, T. M. Brocher, and J. Hardebeck
Table 1
A Subset of the Previous Studies on Seismic Velocity Structure in California
Study Area
References
Coalinga
Coast Ranges
Coso geothermal area
Coyote Lake
Great Valley
Greater Los Angeles basin
Loma Prieta
Monterey Bay
Parkfield region
San Francisco Bay region
Santa Monica Mountains
Sierra Nevada arc
Entire southern California
Eberhart-Phillips (1990)
Eberhart-Phillips (1986); Henstock et al.(1997); Bleibinhaus et al.(2007)
Hauksson and Unruh (2007)
Thurber (1983)
Hwang and Mooney (1986); Godfrey et al. (1997)
Magistrale et al. (1996); Hauksson and Haase (1997); Lutter et al. (1999)
Foxall et al. (1993); Thurber et al. (1995); Eberhart-Phillips and Michael (1998)
Begnaud et al. (2000)
Eberhart-Phillips and Michael (1993); Thurber et al. (2003, 2006)
Manaker et al. (2005); Hardebeck et al. (2007); Thurber et al (2007)
Lutter et al. (2004)
Brocher et al. (1989); Fliedner et al. (1996, 2000); Boyd et al. (2004)
Hauksson (2000); Huang and Zhao (2003); Zhou (2004)
3D Coarse Model
Because of the large spatial scale and amount of data in
our study, we first solve for a coarse 3D V P model starting
with a one-dimensional (1D) velocity model (shown in the
small panel of Fig. 2d) for the entire state. This 1D model
is based on standard regional 1D velocity models used to locate earthquakes by the seismic networks in northern and
southern California. The starting model nodes (shown in
Fig. 2d) are uniformly spaced at 30 km intervals in the horizontal directions and extend 570 km in the SW–NE direction and 1320 km in the NW–SE direction. In the vertical
direction, the nodes are positioned at 1, 1, 4, 8, 14, 20, 27,
35, and 45 km (relative to mean sea level). We only use
absolute arrival times for this 3D coarse model. An a priori
Moho is not included at this stage, but is introduced later for
the finer-scale model. Preliminary inversions were carried
out using the tomography algorithm simul2000 (Thurber
and Eberhart-Phillips, 1999). This algorithm simultaneously
solves for 3D velocity structure and earthquake locations
using the first-arrival times employing an iterative dampedleast-squares method. This step was taken for data quality
control purposes (i.e., identifying poorly constrained events
and picks with very high residuals), and to provide formal
but approximate estimates of velocity model resolution
and uncertainty. After the data quality control step using
simul2000, we applied the regional-scale DD tomography
algorithm, which is more suitable for the large-scale area
Table 2
Active-Source Data Sets Included in the Statewide Tomographic Inversion
Experiment Name
Reference
Year
No. Shots
No. Stations
USGS
Geysers-San Pablo Bay
Oroville
Imperial Valley
Western Mojave Desert
Gilroy-Coyote Lake
Livermore
Great Valley
San Juan Bautista
Shasta 1981
Shasta 1982
Morro Bay
Coalinga
Long Valley
San Luis Obispo
Loma Prieta
San Francisco Bay 1991
PACE 1992
Southern Sierra
San Francisco Bay 1993
LARSE 1994
LARSE 1999
Parkfield
Network
Warren (1978)
Warren (1981)
Spieth et al. (1981)
Kohler and Fuis (1988)
Harris et al.(1988)
Mooney and Luetgert (1982)
Williams et al. (1999)
Murphy (1989); Colburn and Walter (1984)
Mooney and Colburn (1985)
Kohler et al. (1987)
Kohler et al. (1987)
Murphy and Walter (1984)
Murphy and Walter (1984)
Meador et al. (1985)
Sharpless and Walter (1988)
Brocher et al. (1992)
Murphy et al.(1992); Kohler and Catchings (1994); Brocher and Pope (1994)
Fliedner et al. (1996)
Fliedner et al. (1996)
Catchings et al. (2004)
Murphy et al. (1996)
Fuis, Murphy,et al. (2001)
Thurber et al. (2003, 2004); Hole et al. (2006)
Northern and Southern California Earthquake Data Center
1967
1976
1977
1979
1980
1980/1981
1980/1981
1981/1982
1981/1982
1981
1982
1982
1983
1983
1986
1990
1991
1992
1993
1993
1994
1999
2003
1976–2003
9
5
5
41
10
4
3
7
6
1
9
9
9
9
10
2252
6
5
23
14
125
78
157
270
147
135
118
932
245
236
251
221
335
274
299
230
209
278
123
16
300
384
1241
399
889
925
242
659
A California Statewide Three-Dimensional Seismic Velocity Model
in this study. To make the inversion more stable, some regularization method is required, such as smoothing and
damping. Smoothing regularization provides a minimumfeature model that contains only as much structure as can
be resolved above the estimated level of noise in the data
(Zhang and Thurber, 2003). Damping and smoothing are
often selected empirically, by running a series of singleiteration inversions with a large range of values, and plotting
the data variance versus model variance trade-off curves
(e.g., Eberhart-Phillips, 1986, 1993). We explored a wide
range of damping (from 25 to 1000) and smoothing (from 0
to 1000) to make sure that we looked at the entire trade-off
curve instead of a portion of it. The smoothing constraint
weighting of 100 (same for the horizontal and vertical directions) and the damping parameter of 350 were chosen by
examining these trade-off curves, which produced good
compromises between data misfit and model variance (see
Ⓔ Figure S1 in the electronic edition of BSSA).
3D Starting Model Adjustments
Our preliminary modeling work did not include an a
priori velocity increase at the Moho, but first-arrival bodywave tomography by itself was not capable of imaging sharp
discontinuities. Thus, after we obtained the 3D coarse velocity
model, we introduced an a priori Moho interface (see Ⓔ
Figure S2 in the electronic edition of BSSA) from the results
of Fuis and Mooney (1990), which was a modification of
Mooney and Weaver (1989). We set the velocity to 8 km=sec
in the model layer right below the Moho and 8:2 km=sec at the
229
deepest layer with a linear gradient for the layers between
these two layers. In order to start with a conservative 3D
model, we removed the low-velocity anomalies in the 3D
coarse model, that is, we require that velocity is initially a
monotonically increasing function of depth. The resulting adjusted 3D model is the starting model for our final P velocity
model. Figure 3a shows the map view of this model at 4 km
depth, with the layer-average velocity values in the inset of
Figure 3b. In order to check the effects of the inclusion of
the Moho interface on our final results, we compared our
final model with a model obtained without a Moho (lowvelocity anomalies are still removed). The two models are
quite similar over well-resolved areas and the model differences between the initial models are reduced after the inversion, indicating that our process converges. Ⓔ Table S1 in the
electronic edition of BSSA shows a comparison of models
with and without the inclusion of a Moho interface.
In order to use differential times to obtain a finer-scale
model given our computer memory limitations, we split the
entire state into five subregions (Fig. 3a). The adjacent subregions overlap by about 30 km. We use the same depth layers
as the coarse model. Figure 3b shows the event and station
distributions for subregion 1 as an example. For each subregion inversion, we use absolute and differential times from
events inside the subregion (blue circles in Fig. 3b) that are
recorded by all the stations (black triangles) and only absolute
times from events outside of the subregion (pink circles) that
are recorded by stations inside of the subregion. In this way,
we improved the resolution of the resulting velocity model for
Figure 3. (a) Map view of the 3D coarse velocity model at 4 km depth and the boundaries of the 5 subregions. (b) Event and station
distribution in the subregion 1 (small panel shows the 1D layer-average velocity). Yellow squares: finer inversion nodes inside of subregion;
green squares: nodes with fixed velocities; blue circles: earthquakes inside of subregion 1; pink circles: earthquakes outside of subregion 1
but recorded by stations inside of the subregion; black triangles: permanent and temporary stations; red stars: active sources (shots and quarry
blasts). Please refer to the text for more details.
G. Lin, C. H. Thurber, H. Zhang, E. Hauksson, P. M. Shearer, F. Waldhauser, T. M. Brocher, and J. Hardebeck
(a)
Normalized Histogram
the deeper layers due to the inclusion of substantial data at
large epicentral distances. We also include all available explosion and quarry data for each subregion (red stars). Inside of
each subregion, the horizontal nodes are spaced at 10 km
intervals in the areas with dense data coverage and 20 km
in other areas (yellow squares). The node spacing outside
of each subregion is 30 km from the coarse model (green
squares). The initial velocity value at each node is computed
from the velocity values at the surrounding eight nodes of the
coarse initial model using trilinear interpolation as described
in Thurber and Eberhart-Phillips (1999). The velocities outside of each subregion are fixed during the inversion of the
inside-subregion velocities. We inverted five local models
separately; our final statewide velocity model is a stitched version of all the five subregion models. The velocities in the
areas of overlap are computed as the average velocities of
the two adjacent subregions. In order to test the robustness
of our stitching approach, we inverted a model that includes
subregions 1 and 2 and compared the resulting model with the
stitched model. The two models are quite similar with some
minor differences that are likely caused by different regularization parameters, which are determined individually for
each inversion by examining data variance versus model
variance trade-off curves.
(1) RMS=1.263 s
0.15
0.1
0.05
0
−2
−1
0
1
2
1
2
1
2
residual (s)
(b)
Normalized Histogram
230
(2) RMS=0.374 s
0.15
0.1
0.05
Model Quality and Resolution
0
−2
−1
0
residual (s)
(c)
Normalized Histogram
The quality of our model can be evaluated by its ability
to (1) fit the observed arrival-time data, and (2) produce
accurate locations for onland controlled-source explosions
that have known coordinates. Figure 4 shows a comparison
of the arrival-time residual distribution before (a) and after
the coarse (b) and final (stitched) (c) 3D velocity inversions
for the entire data set (including controlled sources). The
root-mean-square (rms) misfit is reduced by over a factor
of 3, from 1.26 sec to 0.37 sec, after the 3D coarse model
inversion, and then to 0.32 sec after the final model inversion. The reason that the fit to absolute times in the subregion
model inversions is only slightly better than the coarse model
fit is because the purpose of this step is to improve fine-scale
velocity resolution by using differential times. A hierarchical
weighting scheme is applied with greater weight to the
absolute data for the first two iterations and greater weight
to the differential data for the next four iterations. Note that
most of the improvement of arrival-time fit after the 3D final
model inversion is mainly due to the lower differential time
residuals, where the rms misfit of the differential times is
reduced from 0.28 sec to 0.11 sec.
We independently located the onshore explosions using
the starting 1D and the coarse and final 3D velocity models
and then calculated the horizontal and vertical location
differences between the relocations and the known true locations. Figure 5 shows histograms of shot location accuracy
relocated using the starting 1D model compared with the two
3D models for both horizontal and vertical coordinates. The
horizontal location errors are all positive; the vertical errors
(3) RMS=0.320 s
0.15
0.1
0.05
0
−2
−1
0
residual (s)
Figure 4. The arrival-time residual distribution for the entire
data set (including controlled sources) (a) before 3D velocity inversion; (b) after 3D coarse model inversion; (c) after 3D final model
inversion.
are positive when the assigned location is deeper than the
true location and negative when the assigned location is shallower than the true location. For the 1D model, the error distributions are quite broad, with a mean error of 1.23 km, and
a standard deviation of 1.08 km horizontally. The vertical
error distribution has peaks at about 0.6 and 4.5 km, a mean
(absolute) error of 2.19 km, and a standard deviation of
A California Statewide Three-Dimensional Seismic Velocity Model
(a)
231
(b)
300
STD=1.08 km
250
STD=2.38 km
250
200
Number
Number
200
150
150
100
100
50
50
1D
0
0
1
2
3
4
5
6
1D
0
7
0
2
Horizontal Error (km)
(c)
4
6
8
10
Vertical Error (km)
(d)
300
STD=0.59 km
250
STD=0.82 km
250
200
Number
Number
200
150
150
100
100
50
50
3D Coarse
0
0
1
2
3
4
5
6
3D Coarse
0
7
0
2
Horizontal Error (km)
(e)
4
6
8
10
Vertical Error (km)
(f)
300
STD=0.39 km
250
STD=0.41 km
250
200
Number
Number
200
150
150
100
100
50
50
3D Final
0
0
1
2
3
4
5
6
3D Final
7
Horizontal Error (km)
0
0
2
4
6
8
10
Vertical Error (km)
Figure 5. Histograms of the differences between relocations and known true locations for onland explosions. The two columns are for
horizontal and vertical location errors, respectively. (a) and (b) 1D model; (c) and (d) 3D coarse model; (e) and (f) 3D final model.
2.38 km. In contrast, the 3D coarse model error distributions
are peaked between 0 and 1 km, with mean errors of 0.60 and
0.32 km, and standard deviations of 0.59 and 0.82 km for the
horizontal and vertical errors, respectively. Although this
model is coarse, the 3D shot relocations are significantly
improved, especially in depth. This is because a single
1D-velocity model cannot account for lateral heterogeneity
in velocity structure across all of California. Further, the
3D final model location error distributions are peaked around
0.2 km, with mean errors of 0.35 and 0.15 km and standard
deviations of 0.39 and 0.41 km for the horizontal and vertical
errors, respectively. The poorly located shots fall into several
232
G. Lin, C. H. Thurber, H. Zhang, E. Hauksson, P. M. Shearer, F. Waldhauser, T. M. Brocher, and J. Hardebeck
categories. One group is distant shots recorded on permanent
network stations for cases in which we were not able to obtain the corresponding refraction profile picks. An example is
the shots from the PACE 1992 project (Fliedner et al., 1996).
Others are cases for which data for a particular shot were split
into two separate events, due to the fact that the data were
obtained and entered into the database separately. Examples
are a number of shots from the Parkfield area and several
LARSE shots. Finally, there are a few shots for which only
profile picks are available, and the recording geometry is too
poor to constrain the locations adequately. The reduction in
relocation errors of about a factor of 2 over the 3D coarse
model indicates that our final model significantly improves
resolution for the lateral heterogeneities in the 3D velocity
structure, especially at shallow depths.
To assess the model quality, we performed a restoration
and a checkerboard resolution test similar to those in Thurber
et al. (2009). In the restoration test, event hypocenters, station
locations, and synthetic travel times, calculated from the final
inverted model, have the same distribution as the real data. We
followed the same inversion strategies as those for the real
data and examined the recovering ability of our algorithms.
The inverted final model is similar to the true model over
well-resolved areas (see Ⓔ Figure S3 in the electronic edition
of BSSA). In the checkerboard test, the synthetic times are
computed through the 1D starting velocity model with
5% velocity anomalies across three grid nodes. The results
are shown in Figure S4 (see the Ⓔ electronic edition of BSSA).
Note that in this test, we did not include the Moho interface,
but still removed low-velocity anomalies as was done for the
real data inversion. Some smearing is still seen, part of which
is likely due to the interpolation of velocities when obtaining
the starting velocities for subregion models.
Final P-Wave Velocity Model
Map Views. Figure 6 shows map view slices through the
resulting tomographic P velocity model. Pink dots in each
figure represent earthquakes relocated within 1 km of each
layer depth. The white contours enclose the areas where the
derivative weight sum (DWS; Thurber and Eberhart-Phillips,
1999) is greater than 300. Derivative weight sum measures
the sampling of each node and serves as an approximate
measure of resolution (Zhang and Thurber, 2007). Areas
with DWS values above 300 correspond to well-resolved
areas in the synthetic tests. In the following, we show average velocities at each layer computed for these areas. In order
to quantitatively compare our model with previous tomography models, we interpolated the southern and northern
California models by Lin et al. (2007) and Thurber et al.
(2009) onto our inversion grids and calculated the correlation
coefficients at each layer depth. We will refer to these two
models as the SC and NC models in the following.
Figure 6a,b shows the P-wave velocities in the top two
layers of our model. The average velocity values are
5:26 km=sec at 1 km and 6:0 km=sec at 4 km depth. The ve-
locities in these shallow layers generally correlate with the
surface geology. Lower values are observed in basin and
valley areas, such as the Great Valley, southern San Joaquin
Valley, Ventura basin, Los Angeles basin, and Imperial Valley,
whereas relatively higher velocities are present in the mountain ranges, such as the northern Coast Ranges, Transverse
Ranges, Peninsular Ranges, and Sierra Nevada. The correlation coefficients for the well-resolved areas of these two layers
between our model and the NC model are 0.49 and 0.56,
respectively. The relatively low correlations for these two
layers are mainly due to the low-velocity anomalies in the
Great Valley and fast anomalies in the Sierra Nevada in our
model. The lowest velocity anomalies (about 2:9 km=sec)
appear in the Great Valley and southern San Joaquin Valley.
However, these slow anomalies are at the edge of our wellresolved areas because of the sparse event distribution in this
region. Fairly high-velocity anomalies (∼6:0 km=sec) at 1 km
depth in the Klamath Mountains and Mount Shasta area are
observed that are consistent with the results from seismicrefraction and gravity data in this area (Zucca et al., 1986; Fuis
et al., 1987), but are not seen in the recent northern California
P-wave velocity model by Thurber et al. (2009). This highvelocity body extends to 14 km depth in our model, reaching
∼6:5–6:7 km=sec at 4 km, ∼6:7–7:1 km=sec at 8 km, and
∼7–7:1 km=sec at 14 km depth, with relatively little structural
variations along the north-south direction. These velocities
are consistent with the conclusion by Fuis et al. (1987),
who argued that an imbricated stack of oceanic rock layers
underlies the Klamath Mountains. Another high-velocity
anomaly zone is apparent at 1 and 4 km depth in the Lake
Oroville area. The ∼6:8 km=sec velocity at 4 km depth is generally consistent with the observations by Spieth et al. (1981)
that the velocity is of the order of 7:0 km=sec at a depth of
5 km. This high-velocity anomaly (∼6:9 km=sec) extends
to 8 km depth in our model. The high velocities at 1 km depth
in the southern Sierra Nevada area, ranging from 5:2 km=sec
to 5:8 km=sec, are consistent with the results of Fliedner et al.
(1996, 2000). The velocities at 4 km depth are generally higher than those estimated by Thurber et al. (2009) (∼6:0 km=sec
compared with ∼5:3 km=sec); our model is more consistent
with the results based on the active seismic refraction experiment by Fliedner et al. (1996, 2000).
In southern California, the correlation coefficients for
these two layers between our model and the SC model are
0.65 and 0.56, respectively. Note that these coefficients are
computed over the resolved areas in the model of Lin et al.
(2007), corresponding to the area of X 100 to 200 km
and Y 620 to 100 km. Near-surface velocities in our
model are also relatively high in the western Mojave Desert
in our model. The anomalies are slightly higher than previous
results (e.g., Hauksson, 2000; Lin et al., 2007). We think this
may be due to the inclusion of the active-source data in this
area, which were not used before. In the Imperial Valley area,
the slowest velocity at 1 km depth is 3:07 km=sec in this
study, but about 3:6 km=sec at the surface in Lin et al.
(2007), who concluded that their model slightly overestimates
A California Statewide Three-Dimensional Seismic Velocity Model
Figure 6.
233
Map views of the P-wave velocity model at different depth slices. The white contours enclose the areas where the derivative
weight sum is greater than 300. The average velocities are computed over these areas. Pink dots represent relocated earthquakes. Black lines
denote coast line and lakes, gray lines rivers and surface traces of mapped faults.
(Continued)
234
G. Lin, C. H. Thurber, H. Zhang, E. Hauksson, P. M. Shearer, F. Waldhauser, T. M. Brocher, and J. Hardebeck
Figure 6.
Continued.
A California Statewide Three-Dimensional Seismic Velocity Model
the near-surface velocity compared with seismic refraction
results (Fuis et al., 1984). The reduction of this overestimation
indicates that our model has better resolution for near-surface
structure. The southern San Joaquin Valley is better resolved
in this new model, which is at the northern boundary of the
study area in Lin et al. (2007).
Figure 6c,d shows map views for 8 and 14 km
depths, with average velocity values of 6:26 km=sec and
6:46 km=sec, respectively. These layers are the two bestresolved layers in our model because of the abundant seismicity at these depths, and the results are generally quite
compatible with previous tomographic results. At 8 km depth,
a strong velocity contrast is apparent between the Great Valley
and the Sierra Nevada. At 14 km depth, some of the features
we imaged for the shallow layers are reversed, that is, the basin
and valley areas show relatively high-velocity anomalies and
lower values are present under the mountain ranges. The
reversal of the velocity anomalies associated with most of the
major basins is also observed in previous southern and northern California tomography studies (Lin et al., 2007; Thurber
et al., 2009). The correlation coefficients for these two layers
between our model and the NC model are 0.61 and 0.47, and
0.35 and 0.49 with the SC model, respectively. The relatively
poor correlation with the NC model is mainly due to the
slower velocities (∼5%) in the northern Coast Ranges than
what is observed in the Thurber et al. (2009) model. The
correlation coefficients with the SC model are reduced
compared with the shallower layers. For these two layers,
our model is generally faster than the Lin et al. (2007) model
by about 5% in the basin areas, such as the Ventura basin, Los
Angeles basin, and Imperial Valley.
Map views for the 20 and 27 km depth layers are shown
in Figure 6e,f, with average velocity values of 6:81 km=sec
and 7:28 km=sec, respectively. The correlation coefficients
for these two layers between our model and the NC model
are 0.65 and 0.72, respectively. The resolution of the southern California model by Lin et al. (2007) is poor below
17 km depth, so we focus on the comparison in northern
California. At 20 km depth, the model is consistent with
235
the results of Thurber et al. (2009), but is slightly slower
in the center of the Great Valley. At 27 km depth, the Sierra
Nevada area shows about 6:0 km=sec low-velocity anomalies, but in the same area, the velocity in Thurber et al.
(2009) is about 6:5 km=sec. Our model extends to 45 km
depth. Figure 6g,h shows the map views of the last two layers
at 35 km and 45 km depths. Although the model is not resolved nearly as well as the shallower layers, we are able to
see the low-velocity anomalies in the Sierra Nevada region;
the correlation coefficients for these two layers between our
model and the NC model are 0.70 and 0.46, respectively.
Cross Sections. We present three cross sections to illuminate the large-scale features of the model. One is parallel
to the San Andreas fault (SAF; X 0 km in the Cartesian coordinate system), and the other two are perpendicular to the
SAF (Y 210 km and Y 30). A complete set of cross
sections is provided in the Ⓔ electronic edition of BSSA.
In Figure 7 we show the velocity cross sections through
the resulting model along the three profiles whose locations
are shown in Figure 1.
The X 0 km section in Figure 7a starts in the northern Coast Ranges where intermediate velocities (V P <
6:2 km=sec) extend into the lower crust. At depths greater
than 20 km, the seismicity and high velocities of the subducting Gorda Plate are visible. From Y ∼ 350 to 210 km, the
low near-surface velocities of the Great Valley and southern
San Joaquin Valley sediments and sedimentary rocks are
evident, extending to depths of ∼10 km in the northwest
and to ∼4 km in the southeast. High-velocity rocks (V P ∼
6:5 km=sec) of the underlying Great Valley ophiolite body
are present throughout this part of the section. The section
crosses the Garlock fault (Y ∼ 210 km) and the SAF
(Y ∼ 255 km), where upper and midcrustal velocities are
relatively low (V P < 6:3 km=sec), and then cuts through the
San Gabriel Mountains (SGM) and Peninsular Ranges where
the upper crust velocities are relatively high (V P >
6:2 km=sec) at shallow depths. Beneath the SAF and SGM,
a strong low-velocity zone is apparent, as identified in
Figure 7. Cross sections of the absolute P-wave velocity along the three profiles shown in Figure 1. Again, the pink dots represent
relocated earthquakes and the white contours enclose the area where the derivative weight sum is less than 300. Color scale is the same as in
Figure 6. Abbreviations: C, Calaveras fault; E, Elsinore fault; GF, Garlock fault; G, Greenville fault; H, Hayward fault; SAF, San Andreas
fault; SFB, San Francisco Bay; SGM, San Gabriel Mountains; SS, San Simeon; WN, Whittier Narrows.
236
G. Lin, C. H. Thurber, H. Zhang, E. Hauksson, P. M. Shearer, F. Waldhauser, T. M. Brocher, and J. Hardebeck
previous studies in this area, which has been interpreted to
indicate fluids (e.g., Ryberg and Fuis, 1998; Fuis et al.,
2000).
The section in Figure 7b cuts across the seismically
quiet southern San Francisco (SF) Peninsula and SF Bay
(X 120 to 90 km) and then reaches the seismically
active Hayward, Calaveras, and Greenville faults beneath
the East Bay (X 70 to 30 km). The section then enters
the Great Valley, where the high-velocity basement, thought
to be ophiolite (e.g., Godfrey et al., 1997), shallows to the
northeast (X 30 to 50 km). After that, the section
enters the Sierra Nevada where a thicker crust with a velocity
of ∼6:2 km=sec extends to 32 km depth. The section in
Figure 7c passes through the seismic activity of San Simeon
(X 120 km), Parkfield (X 75 km), and Coalinga
(X 30 km). Even with the 10 km model gridding, the
velocity contrast across the San Andreas at Parkfield is
evident (southwest side faster, e.g., Thurber et al., 2006).
In this section as well, the high-velocity Great Valley ophiolite body is evident with a predominantly southwestern dip of
its upper surface, consistent with potential field data (Jachens
et al., 1995). At X ∼ 50 km, we see a transition to the slower,
thicker crust of the Sierra Nevada.
Figure 8.
S-Wave Velocity Model
Although S-wave velocity models in northern California
are available from ambient noise and surface wave data
(e.g., Yang et al., 2008), there is no 3D model based on
regional network data. In this study, we use the S first-arrival
times from the SCSN and USArray to solve for a V S model.
Note that these data are different from those used for the V P
model. Figure 8a shows the 1020 SCSN and 1292 USArray
events with at least 4 P and 4 S picks. Due to the sparse
distribution of the data, we use the velocity inversion nodes
of the 3D coarse V P model (i.e., 30 by 30 km horizontal node
spacing). The starting S velocities are derived from our
resolved V P model and a constant V P =V S of 1.73. The resolution estimated by the DWS values is quite poor. In order
to test the robustness of the S model, we also start with the S
velocity values from the ambient noise and teleseismic
multiple-plane-wave tomography results by Yang et al.
(2008). The well-resolved part agrees with the results starting
with the constant V P =V S , indicating that the model is relatively robust. Figure 8b shows the map view of our resolved
V S model at 8 km depth. The white contours enclose the area
where the derivative weight sum is greater than 100. We also
compared our V P and V S models to the empirical V P V S
(a) Event distribution for V S model. The red and blue circles represent the events from the USArray and SCSN, respectively.
(b) Map view of our resolved V S model at 8 km depth. Areas where the derivative weight sum is greater than 100 are shown. The average
velocity is computed over these areas. The pink dots represent relocated earthquakes.
A California Statewide Three-Dimensional Seismic Velocity Model
relation of Brocher (2005). This relation is derived from a
diverse dataset, including wireline borehole logs, vertical
seismic profiles, laboratory measurements, and seismic
tomography models, and can be used to infer V S for the
entire Earth’s crust from V P . Using the layer-average P
velocities as inputs, we obtained the corresponding empirical
S velocities. Our comparison indicates that the tomographybased V S results are faster than predicted by the empirical
relation at 1 and 35 km depth, and lower than expected at
8 km depth. Due to the poor resolution of this model, we
do not attempt to solve for Poisson’s ratio and other parameters that depend on V P =V S values. A complete set of map
views and cross sections of our S-wave model is provided in
the Ⓔ electronic edition of BSSA).
Discussion
Our model is the first 3D seismic velocity model for the
entire state of California based on local and regional arrivaltime data. It has improved areal coverage compared with the
previous northern and southern California models, and extends to greater depth due to the inclusion of substantial data
at large epicentral distances. The combination of northern,
southern, and central California data sets results in betterresolved velocity structure at the study boundaries of previous tomographic models, such as the San Joaquin Valley
and southern Sierra Nevada. Because of the 10 km horizontal
grid spacing in our model inversion, which is larger than the
distance cutoff of most waveform cross-correlation calculations (≤ 5 km), we did not apply any differential times from
cross-correlation in this study. There may be some finer-scale
structures that are not resolved due to the data and grid spacing used in our model. We compared our model with some
results based on refraction and/or reflection data. Our model
generally agrees with most of the studies, such as in the Diablo and Gabilan Ranges (Steppe and Robert, 1978; Walter
and Mooney, 1982), the Coyote Lake (Mooney and Luetgert,
1982), the Long Valley (Luetgert and Mooney, 1985), the
San Francisco Bay area (Holbrook et al., 1996), the southern
Sierra (Fliedner et al., 1996), and the Mojave Desert (Fuis,
Ryberg, et al., 2001); but slightly overestimates near-surface
velocity values in some basins and valleys, such as in the
Imperial Valley (McMechan and Mooney, 1980; Fuis et al.,
1984), the Great Valley (Colburn and Mooney, 1986), the
Livermore area (Meltzer et al., 1987), and the greater Los
Angeles basin (Fuis, Ryberg, et al., 2001b).
The differences between this statewide velocity model
and previous regional-scale models are due to several factors,
such as data sets, grid spacing (cell size), tomographic algorithms, and inversion parameters (e.g., damping, smoothing,
and residual weighting). The model is very similar to the
recent northern California model by Thurber et al. (2009)
for the middle to lower crust because the two studies use
the same type of data sets (both absolute and differential
times) and inversion algorithm (tomoFDD), whereas the
southern California model by Lin et al. (2007) is derived
237
by applying the SIMULPS algorithm (Thurber, 1983, 1993;
Eberhart-Phillips, 1990; Evans et al., 1994) to absolute
arrival times for composite events. We also calculated the
correlation coefficients, which are 0.67, 0.56, 0.36, 0.54,
and 0.69 for the top five layers, between our model and
the SCEC unified velocity model (Version 4, Magistrale et al.,
2000). Note that the SCEC model is based on geotechnical
borehole seismic velocity data and the regional tomographic
model of Hauksson (2000), which is also obtained by applying the SIMULPS algorithm. The slightly better correlation at
1 km depth is due to the low-velocity anomalies in the basin
areas. Our new model is generally consistent with these previous results. The improved resolution of our model in nearsurface layers over the previous California tomographic
models is mainly due to the large amount of active-source
data in this study.
The goal of this study is not to replace the previous
tomographic models in California that have more detail than
can be resolved by our data and grid spacing, but to image
the entire state of California at a regional scale, to reveal
some features that are difficult to resolve in local studies,
and to provide the geophysical community with a velocity
model that should be useful for regional-scale studies, such
as regional waveform modeling. The model is available in
the Ⓔ electronic edition of BSSA.
Conclusions
We have developed statewide body-wave tomography
models (P and S) for California using absolute and differential arrival times from earthquakes, controlled sources, and
quarry blasts. By merging the data sets from networks
in northern, southern, and coastal central California and
USArray, we have achieved relatively complete coverage
of the entire state for V P. By including a large amount of
active-source data in this study, we obtained improved resolution in near-surface layers over the previous California
tomographic models, especially in the largest sedimentary
basins, such as the Great Valley, the Imperial Valley, and
the Los Angeles basin. At 8 km depth, there is a clear north
to south increase in the average velocity of the Coast Range
Mountains extending from the Mendocino Triple Junction to
the border with Mexico. At 14 and 20 km depths, the basin
and valley areas show relatively high-velocity anomalies,
with lower velocities present under the mountain ranges.
The Great Valley ophiolite body and the subducting Gorda
Plate are evident from the cross sections. Low-velocity
anomalies in the Sierra Nevada exist from midcrustal to
greater depths; the slow velocity root over this area is the
largest anomaly at 35 km depth. Our model provides a reasonable fit to the data and relocates explosions, treated as
earthquakes, with an absolute accuracy of better than a
kilometer. Thus, it should be useful for producing a statewide earthquake location catalog based on a single velocity
model.
238
G. Lin, C. H. Thurber, H. Zhang, E. Hauksson, P. M. Shearer, F. Waldhauser, T. M. Brocher, and J. Hardebeck
Data and Resources
Active-source data used in this study were collected from
published studies listed in the references. Catalog picks were
obtained from the USArray, the Northern California Earthquake Data Center (NCEDC), and the Southern California
Earthquake Data Center (SCEDC) and originate principally
from the Northern California Seismic Network (NCSN) and
Southern California Seismic Network (SCSN). Some figures
were made using the public domain Generic Mapping Tools
software (Wessel and Smith, 1991).
Acknowledgments
We thank the U.S. Geological Survey (USGS) and Caltech staff for
maintaining the NCSN and SCSN, and the IRIS Data Management Center
for making USArray data available. R. Catchings,C. Evangelidis, A. Frankel,
G. Fuis, S. Hartzell, W. Kohler, A. Lindh, J. Murphy, D. O’Connell, and
T. Parsons contributed first-arrival times and receiver and source locations
for active-source experiments in the study area. We thank W.-X. Du for
his effort to assemble the northern California active-source data set into a consistent form and Y. Yang for providing his ambient noise tomography model.
This work is supported by the National Earthquake Hazards Reduction program, under USGS awards 07HQGR0038, 07HQGR0045, 07HQGR0047,
07HQGR0050, 08HQGR0032, 08HQGR0039, 08HQGR0042 and
08HQGR0045, and the National Mapping Programs of the USGS. The views
and conclusions contained in this document are those of the authors and
should not be interpreted as necessarily representing the official policies,
either expressed or implied, of the U.S. government.
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Department of Geoscience
University of Wisconsin–Madison
1215 W. Dayton St.
Madison, Wisconsin 53706
(G.L., C.H.T.)
Department of Earth, Atmospheric, and Planetary Sciences
Massachusetts Institute of Technology
77 Massachusetts Avenue, 54-1818
Cambridge, Massachusetts 02139
(H.Z.)
Seismological Laboratory
California Institute of Technology
1200 E. California Boulevard
Mail Code 252–21
Pasadena, California 91125
(E.H.)
Institute of Geophysics and Planetary Physics
Scripps Institution of Oceanography
University of California, San Diego
La Jolla, California 92093–0225
(P.M.S.)
Lamont-Doherty Earth Observatory
Columbia University
Palisades, New York 10964
(F.W.)
U.S. Geological Survey
345 Middlefield Road, MS 977
Menlo Park, California 94025
(T.M.B., J.H.)
Manuscript received 23 January 2009